Pointwise Green's function bounds and stability of relaxation shocks

Details Pointwise Green's function bounds and stability of relaxation shocks Pointwise Green's function bounds and stability of relaxation shocks

2001-07-13

arxiv.org/abs/math/0107107v4

Mathematics

Analysis of PDEs

120 pages. Changes since original submission. Corrected typos, esp. energy estimates of Section 7, corrected bad forward refer

Scientific paper

We establish sharp pointwise Green's function bounds and consequent linearized and nonlinear stability for smooth traveling front solutions, or relaxation shocks, of general hyperbolic relaxation systems of dissipative type, under the necessary assumptions ([G,Z.1,Z.4]) of spectral stability, i.e., stable point spectrum of the linearized operator about the wave, and hyperbolic stability of the corresponding ideal shock of the associated equilibrium system. This yields, in particular, nonlinear stability of weak relaxation shocks of the discrete kinetic Jin--Xin and Broadwell models. The techniques of this paper should have further application in the closely related case of traveling waves of systems with partial viscosity, for example in compressible gas dynamics or MHD.

Affiliated with

Also associated with

No associations

Rating

Pointwise Green's function bounds and stability of relaxation shocks does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Pointwise Green's function bounds and stability of relaxation shocks, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Pointwise Green's function bounds and stability of relaxation shocks will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-141375